The pressure at the intersection will be very close to the pressure at the discharge of any of your three pumps.
Are the pipe discharges from the pumps symmetrical (or similar) to the header (intersection)?
Do you know the flow rate of each pump (or the combination?)
Do you have a pump curve for the pumps? (if not ask the manufacturer)
Do you have any pressure readings the the pipe anywhere?
There is no way to mathematically determine the pressure at a given point in a pump system with just the flow rate. My question about the flow rates was leading toward the next question, do you have the pump curves for the centrifugal pumps. If they are putting out 350 m3/hr, then you need only look at the curves to determine the overall system pressure. You can work your way back from there.